Math Problem Statement
Beginning inventory, purchases, and sales for an inventory item are as follows:
DateLine Item DescriptionUnits and CostSep. 1
Beginning Inventory
31 units @ $22
5
Sale
18 units
17
Purchase
33 units @ $24
30
Sale
33 units
Assuming a perpetual inventory system and the first-in, first-out method:
a. Determine the cost of goods sold for the September 30 sale. fill in the blank 1 of 2$
b. Determine the inventory on September 30. fill in the blank 2 of 2$
Solution
We will solve this step by step to determine cost of goods sold (COGS) for the September 30 sale and ending inventory using the First-In, First-Out (FIFO) method.
Step 1: Track Inventory Changes and COGS under FIFO
Since we are using FIFO, the oldest inventory is sold first. Below is the sequence of events:
-
Beginning Inventory (Sep 1):
31 units @ $22 each = 31 × 22 = $682 -
Sep 5 Sale: 18 units
-
Use 18 units from beginning inventory (31 units @ $22).
-
COGS = 18 × 22 = $396
-
Remaining Inventory after Sep 5:
31 - 18 = 13 units @ $22 each = $286
-
-
Sep 17 Purchase: 33 units @ $24 each
-
Add 33 units @ $24 = 33 × 24 = $792
-
Total Inventory after Sep 17:
13 units @ $22 = 286
33 units @ $24 = 792
Total = 13 + 33 = 46 units
Total value = 286 + 792 = $1,078
-
-
Sep 30 Sale: 33 units
-
Follow FIFO (sell older inventory first):
- 13 units @ $22 = 13 × 22 = $286
- Remaining 33 - 13 = 20 units taken from new batch (33 units @ $24): 20 × 24 = $480
-
COGS for Sep 30 Sale = 286 + 480 = $766
-
Step 2: Calculate Ending Inventory on September 30
After the sale on Sep 30, we had 33 units and sold 33 units.
The inventory now looks like this:
-
Used 13 units @ $22
-
Used 20 units from 33 units @ $24
Remaining Inventory = 33 - 20 = 13 units @ $24Total value of ending inventory = 13 × 24 = $312
Answers
a. Cost of Goods Sold (COGS) for Sep 30 Sale = $766
b. Ending Inventory on Sep 30 = $312
Do you want more details or have further questions?
Here are 5 related questions:
- What is the difference between FIFO and LIFO?
- How does perpetual inventory differ from periodic inventory?
- How would COGS change if LIFO were used?
- Why is FIFO commonly used for perishable goods?
- How can inflation impact FIFO-based inventory valuation?
Tip: FIFO generally results in lower COGS and higher profits during periods of rising prices.
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Math Problem Analysis
Mathematical Concepts
Inventory Management
Cost Accounting
Perpetual Inventory System
FIFO Method
Formulas
Cost of Goods Sold (COGS) = Units Sold * Cost per Unit
Ending Inventory = Remaining Units * Cost per Unit
Theorems
First-In, First-Out (FIFO) Method
Suitable Grade Level
College-level Accounting or Business
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